...
By comparing the size of floc particles that both the critical velocity theory and the capture velocity theory should theoretically filter out of the effluent, you can see which theory should govern the plate settler behavior. The equations relating the critical and capture velocity are as follows:
| Latex |
|---|
| Wiki Markup |
{latex} \large % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyuamaaBa % aaleaacaWGJbGaamOCaiaadMgacaWG0bGaamyAaiaadogacaWGHbGa % amiBaaqabaGccqGH9aqpdaWcaaqaaiabec8aWjaadofacaWGwbGaci % 4CaiaacMgacaGGUbGaeqiUde3aaWbaaSqabeaacaaIYaaaaaGcbaGa % aG4maiaaikdacaWGKbWaaSbaaSqaaiaaicdaaeqaaOWaaWbaaSqabe % aacaaIYaaaaOWaamWaaeaadaWcaaqaaiabgkHiTiaaigdacaaI4aGa % amOvaiabfA6agjabe27aUjabeg8aYnaaBaaaleaacaWGibGaaGOmai % aad+eaaeqaaaGcbaGaamizamaaDaaaleaacaaIWaaabaGaaGOmaaaa % kiaadEgacaGGOaGaeqyWdi3aaSbaaSqaaiaadIeacaaIYaGaam4taa % qabaGccqGHsislcqaHbpGCdaWgaaWcbaGaamOraiaadYgacaWGVbGa % am4yaaqabaGccaGGPaaaaaGaay5waiaaw2faamaaCaaaleqabaWaaS % aaaeaacaaIXaaabaGaamiramaaBaaameaacaWGgbGaamOCaiaadgga % caWGJbGaamiDaiaadggacaWGSbaabeaaliabgkHiTiaaigdaaaaaaa % aaaaa!732E! $$ Q_{critical} = {{\pi SV\sin \theta ^2 } \over {32d_0 ^2 \left[ {{{ - 18V\Phi \nu \rho _{H2O} } \over {d_0^2 g(\rho _{H2O} - \rho _{Floc} )}}} \right]^{{1 \over {D_{Fractal} - 1}}} }} $$ {latex} |
| Latex |
|---|
| Wiki Markup |
{latex} \large % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyuamaaBa % aaleaacaWGJbGaamyyaiaadchacaWG0bGaamyDaiaadkhacaWGLbaa % beaakiabg2da9maalaaabaGaamitaiGacogacaGGVbGaai4CaiabeI % 7aXjabgUcaRiaadofaciGGZbGaaiyAaiaac6gacqaH4oqCaeaacaWG % tbaaamaadmaabaGaeqiWda3aaeWaaeaadaWcaaqaaiaadofaaeaaca % aIYaaaaaGaayjkaiaawMcaamaaCaaaleqabaGaaGOmaaaaaOGaay5w % aiaaw2faaiaadAfaaaa!53CA! $$ Q_{capture} = {{L\cos \theta + S\sin \theta } \over S}\left[ {\pi \left( {{S \over 2}} \right)^2 } \right]V $$ {latex} |
Where
S = Tube settler diameter (or spacing)
d0 = size of primary particles
V = Predicted Terminal Velocity
| Latex |
|---|
| Wiki Markup |
{latex} \large % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuOPdyeaaa!3767! $$ \Phi $$ {latex} |
= Shape Factor
Since, with our experiments, all of these variables will be held constant except for the spacing, we can analyze these relationships between critical and capture velocity theories for different tube diameters. The predicted terminal settling velocity is a range from 5 to 100 meters per day. For each spacing, this is what is varied in order to get a range of flow rates to be tested in each ramp state experiment.
...